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Sequential decision-making approach for quadrangular mesh generation

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Abstract

A new indirect quadrangular mesh generation algorithm which relies on sequential decision-making techniques to search for optimal triangle recombinations is presented. In contrast to the state-of-art Blossom-quad algorithm, this new algorithm is a good candidate for addressing the 3D problem of recombining tetrahedra into hexahedra.

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References

  1. Baudouin TC, Remacle JF, Marchandise E, Henrotte F, Geuzaine C (2014) A frontal approach to hex-dominant mesh generation. Adv Model Simul Eng Sci 1(1):1–30

    Article  Google Scholar 

  2. Blacker TD, Stephenson MB (1991) Paving: a new approach to automated quadrilateral mesh generation. Int J Numer Methods Eng 32(4):811–847

    Article  MATH  Google Scholar 

  3. Borouchaki H, Frey PJ (1998) Adaptive triangular-quadrilateral mesh generation. Int J Numer Methods Eng 41(5):915–934

    Article  MathSciNet  MATH  Google Scholar 

  4. Bunin G (2006) Non-local topological clean-up. In: Pébay PP (ed) Proceedings of the 15th International Meshing Roundtable. Springer, pp 3–29

  5. D’Azevedo E (2000) Are bilinear quadrilaterals better than linear triangles? SIAM J Sci Comput 22(1):198–217

    Article  MathSciNet  MATH  Google Scholar 

  6. Frey PJ, Marechal L (1998) Fast adaptive quadtree mesh generation. In: Proceedings of the Seventh International Meshing Roundtable, pp 211–224

  7. Jiménez A, Kiwi M (2011) Counting perfect matchings in the geometric dual. Electron Notes Discret Math 37:225–230

    Article  Google Scholar 

  8. Jung T, Wehenkel L, Ernst D, Maes F (2013) Optimized look-ahead tree policies: a bridge between look-ahead tree policies and direct policy search. Int J Adapt Control Signal Process. Available as preprint at: http://onlinelibrary.wiley.com/ doi:10.1002/acs.2387/full

  9. Kolmogorov V (2009) Blossom V: a new implementation of a minimum cost perfect matching algorithm. Math Program Comput 1(1):43–67

    Article  MathSciNet  MATH  Google Scholar 

  10. Kowalski N, Ledoux F, Frey P (2013) A PDE based approach to multidomain partitioning and quadrilateral meshing. Springer, pp 137–154

  11. Lee CK, Lo SH (1994) A new scheme for the generation of a graded quadrilateral mesh. Comput Struct 52(5):847–857

    Article  MathSciNet  MATH  Google Scholar 

  12. Lévy B, Liu Y (2010) Lp centroidal voronoi tessellation and its applications. ACM Trans Graph 29(4): 119:1–119:11

  13. Lo S, Lee C (1992) On using meshes of mixed element types in adaptive finite element analysis. Finite Elem Anal Des 11(4):307–336

    Article  MATH  Google Scholar 

  14. Maes F, St-Pierre D, Ernst D (2013) Monte carlo search algorithm discovery for single-player games. IEEE Trans Comput Intell AI Games 5(3):201–213. doi:10.1109/TCIAIG.2013.2239295

    Article  Google Scholar 

  15. Meshkat S, Talmor D (2000) Generating a mixed mesh of hexahedra, pentahedra and tetrahedra from an underlying tetrahedral mesh. Int J Numer Methods Eng 49(1–2):17–30

    Article  MATH  Google Scholar 

  16. Owen SJ, Staten ML, Canann SA, Saigal S (1999) Q-Morph: an indirect approach to advancing front quad meshing. Int J Numer Methods Eng 44(9):1317–1340

    Article  MATH  Google Scholar 

  17. Remacle JF, Henrotte F, Carrier-Baudouin T, Bechet E, Marchandise E, Geuzaine C, Mouton T (2013) A frontal delaunay quad mesh generator using the lnorm. Int J Numer Methods Eng 94(5):494–512

    Article  MathSciNet  Google Scholar 

  18. Remacle JF, Lambrechts J, Seny B, Marchandise E, Johnen A, Geuzaine C (2012) Blossom-quad: A non-uniform quadrilateral mesh generator using a minimum-cost perfect-matching algorithm. Int J Numer Methods Eng 89(9):1102–1119

    Article  MathSciNet  MATH  Google Scholar 

  19. Yamakawa S, Shimada K (2003) Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cells. Int J Numer Methods Eng 57(15):2099–2129

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhu J, Zienkiewicz O, Hinton E, Wu J (1991) A new approach to the development of automatic quadrilateral mesh generation. Int J Numer Methods Eng 32(4):849–866

    Article  MATH  Google Scholar 

  21. Zienkiewicz O, Taylor R (2000) The finite element method—the basis, vol 1. Elsevier

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Acknowledgments

This research project was funded in part by the Walloon Region under WIST 3 grant 1017074 (DOMHEX).

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of Liège, Liège, Belgium

    Amaury Johnen, Damien Ernst & Christophe Geuzaine

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  1. Amaury Johnen
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  2. Damien Ernst
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  3. Christophe Geuzaine
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Correspondence to Christophe Geuzaine.

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Johnen, A., Ernst, D. & Geuzaine, C. Sequential decision-making approach for quadrangular mesh generation. Engineering with Computers 31, 729–735 (2015). https://doi.org/10.1007/s00366-014-0383-9

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  • DOI: https://doi.org/10.1007/s00366-014-0383-9

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